Answer to Question #144782 in General Chemistry for Joshua

Question

Titanium metal crystallizes with HCP unit cell. Its radius is 0.1445 nm. Calculate the density of solid crystalline titanium in g/cm^3.

Answer 1

Radius of titanium, R = 0.1445nm

Unit cell volume, V_c = 6R² C√3

For Ti, c/a = 1.58

c = 1.58a

And a = 2R , also c = 3.16R

Vc = 6R² × 3.16R ×√3

= 6×(0.1445×10^-9)² × 3.16(0.1445 ×10^-9) ×√3

= 9.91 ×10^-23cm³

In a unit, you have 6 atoms

Density = mass/volume

Mass = 6× 47.87/ 6.02×10²³

Density = 6 ×47.87/ (6.02×10²³ × 9.91 ×10^-23)

= 4.81gcm^-3